Over the long course of my career I have heard many of my colleagues refer to these two terms interchangeably, although this is actually not true and may cost you a wrong answer on an exam such as Cisco’s CCNA or CCNP which could make the difference between you passing the exam or not. Let us take a look at the differences in these two terms.
The Port resides at layer 1 of the OSI model, the Physical layer. This layer defines the electrical and physical specifications for a device, such as copper or fiber media as well as the voltages, line impedance, signal timing, and the physical layout of pins for the connecting device such as twisted pairs, coaxial or in the case of fiber cable single mode or multi-mode.
The Interface resides at layer 2 of the OSI model, the Data Link layer. This layer defines the functional and procedural method of transferring data between network devices, such as Serial, Ethernet, FDDI, and Token-Ring. Additionally this layer may provide the ability to detect and maybe correct errors that might occur at the physical layer.
There are a number of interfaces that have no physical connection to any device such as Loopbacks, Lines, and VLANs. These interfaces are referred to as virtual interfaces, and although these interfaces have no physical connection they can still be addressed and accessed by other devices in a network. Interfaces such as Loopback interfaces are very useful in insuring devices are reachable with many routing protocols.
Sub interfaces are another form of virtual interface and are used in WAN connections like Frame-Relay, and VLAN Trunks between routers and switches when creating a router on a stick to route between VLANs or deploying DHCP addressing for multiple VLANs.
In conclusion the line between Ports and Interfaces may be blurry, and in the real world the two terms may be used interchangeably but there is a difference and you need to understand the difference not only to pass an exam, but to help you properly configure network interfaces on Cisco routing and switch equipment and help you troubleshoot some complex networking issues. A good way to remember this is you use some form of media to physically connect a network port to another network device port and you configure a network interface with some form of protocol to allow communication between network devices on a LAN or WAN.